The Oddballs is set at the turn of the century, in a small Georgian town blessed with two eccentric individuals who upset the town's settled ways: Christofor and Ertaoz.

Ertaoz's father dies and, true to Georgian custom, he has to pay the dead man's debts. He goes to the city to earn some money, and here, he falls in love with the beautiful Margalita. But the voluptuous redhead has numerous other lovers, amongst them the Governor, who removes his youthful competitor by having him jailed.

In prison, Ertaoz meets Christofor, an old mathematician, who persuades the boy that man can fly. They escape and build an aircraft from oak logs, hides, concrete and iron, with three heaps of wood for fuel, and a full wine-skin. And to everyone's surprise — the weird contraption takes off!